The difference is in the reactions.
Such cartoons offend us both. What is the Jewish reaction? We kvetch. We write about it, maybe even go to court.
What is the Muslim reaction? Violent terrorist attacks, rioting- murder.
No, we are not hypocrites, and yes, we believe in free speech. But we are allowed to be offended, as anyone would be…
Another point in that anti-Semitic cartoons are typically direct against Jews per se, not against the Second Commandment (the one about “graven images”).
It should be noted that the Second Commandment caused trouble over the centuries for Christians too. During the Protestant Reformation, zealous new Bible readers went about smashing statues in churches (called “iconoclasm”). To this day, the stained glass windows of (what were once) the stricter Protestant denominations do not show any figures, just patterns in glass.
The original idea of setting oneself apart from religions with idols seemed like a good idea at the time…but how much relevance does it really have in the 21st century?
Indeed, some Muslims seems to make an idol of the Koran itself, with their rules about how it must handled and their extreme upset about it being burned. Are they not making the book an idol itself?